Linear Equations in Real Life by JohnQuinn

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									        Real World
        Applications of
        Linear Equations
           Yes, there really are uses for them!!



Math 208 ~ College Mathematics I
Objective: Apply the concepts of slope and intercept to real-life situations
    Today’s Objectives
 To define the slope of a
  linear equation a real world
  context
 To find a meaning for an

  equation’s x & y-intercepts
       Brief Review of Graphing
   Solve the equation for y        2x + y = 3

                                    y = – 2x + 3
   Make a table and find       x   y = –2x + 3     y
                               –1
    some ordered pair                y=2+3          5
                                0    Y=0+3          3
    values                      1   Y = –2 + 3      1
                                2   Y = –4 + 3     –1
    Graph the Equation
   Graph the ordered
    pairs
                          (-1, 5)
   Draw the line            (0, 3)
                               (1, 1)
    (shows all the              (2, -1)

    possible solutions)
  First Problem to follow along.
          Use the handout

What do we know?
 A pillow company buys ribbon in 100 foot
  rolls.
 2.5 feet of ribbon are needed to decorate
  each pillow.
What do we need to do?
 Write an equation. Use y for the amount
  ribbon left on the roll and x for the number
  of pillows made.
 Fill in the table and draw the a graph.
Write Equation & Fill in the Table

 # Pillows                    # of Feet of Ribbon
   Made      y = 100 – 2.5x   Remaining on Roll

    0          100 – 0               100
    1          100 – 2.5              97.5
    2          100 – 5                95
    3          100 – 7.5              92.5
    4          100 – 10                90
Draw the graph
    100
     90
     80
     70
     60
     50
     40
     30
     20
     10

          1   2   3   4 5   6   7   8   9 10
   Questions for
                        100

                        90

                        80




   Discussion
                        70

                        60

                        50

                        40

                        30
                                      y = 100 – 2.5x
                        20



1. What is the slope?
                        10



                              1   2    3   4 5   6   7   8   9 10

   What does it represent?
2. Why is the slope negative?
3. What is the y-intercept? What does
   it represent?
4. What is the x-intercept? What does
   it represent?
  Second Problem
What do we know?
  A swimming pool holds 450 gallons of water.

  The pool currently contains 100 gallons of
   water.
  A hose deposits 50 gallons of water in the
   pool each minute.
What do we need to do?
  Write an equation. Use y for the amount of
   water in the pool and x for the number of
   minutes the hose runs.
  Fill in the table and graph the information.
 Fill in the Table

# of Minutes Hose                   # of Liters in
     is in Pool     y = 100 + 50x     The Pool

       0            100 + 0             100
       1            100 + 50            150
       2            100 + 100           200
       3            100 + 150           250
       4            100 + 200           300
Draw the Graph
    500
    450
    400
    350
    300
    250
    200
    150
    100
     50

          1   2   3   4 5   6   7   8   9 10
                     500

                     450




   Questions for     400

                     350




   Discussion
                     300

                     250

                     200

                     150
                                   y = 100 + 50x
                     100




1. What is the slope?
                      50



                           1   2   3   4 5   6   7   8   9 10


2. What does it represent?
3. What is the y-intercept? What
   does it represent?
4. Why does this graph contain a
   line segment (have an end)?
      Conclusions
   What kinds of real life applications are linear?
    (What do these situations have in common?)
    They both have a Constant Rate of Change (SLOPE)
   What does the slope represent?
    The slope represents the rate of change

   What does the y=intercept represent?
    The y-intercept represents the y value before the
    rate begins. x = 0

								
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